Average Error: 1.0 → 0.0
Time: 18.1s
Precision: 64
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
↓
\[\left(\cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}} \cdot \frac{1}{\sqrt{3}}\right) \cdot \cos \left(\frac{2 \cdot \pi}{3}\right) - \left(\sqrt{\sin \left(\frac{2 \cdot \pi}{3}\right)} \cdot \sqrt{\sin \left(\frac{2 \cdot \pi}{3}\right)}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}} \cdot \frac{1}{\sqrt{3}}\right)\right) \cdot 2\]
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
↓
\left(\cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}} \cdot \frac{1}{\sqrt{3}}\right) \cdot \cos \left(\frac{2 \cdot \pi}{3}\right) - \left(\sqrt{\sin \left(\frac{2 \cdot \pi}{3}\right)} \cdot \sqrt{\sin \left(\frac{2 \cdot \pi}{3}\right)}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}} \cdot \frac{1}{\sqrt{3}}\right)\right) \cdot 2
double f(double g, double h) {
        double r5907521 = 2.0;
        double r5907522 = atan2(1.0, 0.0);
        double r5907523 = r5907521 * r5907522;
        double r5907524 = 3.0;
        double r5907525 = r5907523 / r5907524;
        double r5907526 = g;
        double r5907527 = -r5907526;
        double r5907528 = h;
        double r5907529 = r5907527 / r5907528;
        double r5907530 = acos(r5907529);
        double r5907531 = r5907530 / r5907524;
        double r5907532 = r5907525 + r5907531;
        double r5907533 = cos(r5907532);
        double r5907534 = r5907521 * r5907533;
        return r5907534;
}
↓
double f(double g, double h) {
        double r5907535 = g;
        double r5907536 = -r5907535;
        double r5907537 = h;
        double r5907538 = r5907536 / r5907537;
        double r5907539 = acos(r5907538);
        double r5907540 = 3.0;
        double r5907541 = sqrt(r5907540);
        double r5907542 = r5907539 / r5907541;
        double r5907543 = 1.0;
        double r5907544 = r5907543 / r5907541;
        double r5907545 = r5907542 * r5907544;
        double r5907546 = cos(r5907545);
        double r5907547 = 2.0;
        double r5907548 = atan2(1.0, 0.0);
        double r5907549 = r5907547 * r5907548;
        double r5907550 = r5907549 / r5907540;
        double r5907551 = cos(r5907550);
        double r5907552 = r5907546 * r5907551;
        double r5907553 = sin(r5907550);
        double r5907554 = sqrt(r5907553);
        double r5907555 = r5907554 * r5907554;
        double r5907556 = sin(r5907545);
        double r5907557 = r5907555 * r5907556;
        double r5907558 = r5907552 - r5907557;
        double r5907559 = r5907558 * r5907547;
        return r5907559;
}

Error

Bits error versus g

Bits error versus h

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.0

    \[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt1.0

    \[\leadsto 2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\color{blue}{\sqrt{3} \cdot \sqrt{3}}}\right)\]

  4. Applied *-un-lft-identity1.0

    \[\leadsto 2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\color{blue}{1 \cdot \cos^{-1} \left(\frac{-g}{h}\right)}}{\sqrt{3} \cdot \sqrt{3}}\right)\]

  5. Applied times-frac1.0

    \[\leadsto 2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \color{blue}{\frac{1}{\sqrt{3}} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}}}\right)\]
  6. Using strategy rm

  7. Applied cos-sum1.0

    \[\leadsto 2 \cdot \color{blue}{\left(\cos \left(\frac{2 \cdot \pi}{3}\right) \cdot \cos \left(\frac{1}{\sqrt{3}} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}}\right) - \sin \left(\frac{2 \cdot \pi}{3}\right) \cdot \sin \left(\frac{1}{\sqrt{3}} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}}\right)\right)}\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt0.0

    \[\leadsto 2 \cdot \left(\cos \left(\frac{2 \cdot \pi}{3}\right) \cdot \cos \left(\frac{1}{\sqrt{3}} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}}\right) - \color{blue}{\left(\sqrt{\sin \left(\frac{2 \cdot \pi}{3}\right)} \cdot \sqrt{\sin \left(\frac{2 \cdot \pi}{3}\right)}\right)} \cdot \sin \left(\frac{1}{\sqrt{3}} \cdot \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}}\right)\right)\]

  10. Final simplification0.0

    \[\leadsto \left(\cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}} \cdot \frac{1}{\sqrt{3}}\right) \cdot \cos \left(\frac{2 \cdot \pi}{3}\right) - \left(\sqrt{\sin \left(\frac{2 \cdot \pi}{3}\right)} \cdot \sqrt{\sin \left(\frac{2 \cdot \pi}{3}\right)}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{\sqrt{3}} \cdot \frac{1}{\sqrt{3}}\right)\right) \cdot 2\]

Reproduce

herbie shell --seed 2019171 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2.0 (cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))))